Abstract Learning Frameworks for Synthesis

Abstract

We develop abstract learning frameworks for synthesis that embody the principles of the CEGIS counterexample-guided inductive synthesis algorithms in current literature. Our framework is based on iterative learning from a hypothesis space that captures synthesized objects, using counterexamples from an abstract sample space, and a concept space that abstractly defines the semantics of synthesis. We show that a variety of synthesis algorithms in current literature can be embedded in this general framework. We also exhibit three general recipes for convergent synthesis: the first two recipes based on finite spaces and Occam learners generalize all techniques of convergence used in existing engines, while the third, involving well-founded quasi-orderings, is new, and we instantiate it to concrete synthesis problems.